page_title: Spherical Earth
section_title: Grids are distorted by spherical ground
hierarchical_section_title: Spherical Earth / Effects and empirical evidence / Grids are distorted by spherical ground
caption_attribution_description: Illustration of spherical geometry where the angles of a triangle do not sum to 180°. The globe is an orthographic projection centered on Japan at 135°30' E, 36° N. The map is of Oga Peninsula, Akita, Japan at 139°52' E, 39°56' N. Landsat image with high-resolution data from Space Shuttle. This file is intended to replace en:Image:Triangle on globe.jpg, a low-quality file with questionable copyright.
context_page_description: The earliest documented mention of the spherical Earth concept dates from around the 5th century BC, when it was mentioned by ancient Greek philosophers. It remained a matter of speculation until the 3rd century BC, when Hellenistic astronomy established the spherical shape of the Earth as a physical fact and calculated the Earth's circumference. The paradigm was gradually adopted throughout the Old World during Late Antiquity and the Middle Ages. A practical demonstration of Earth's sphericity was achieved by Ferdinand Magellan and Juan Sebastián Elcano's circumnavigation.
  The concept of a spherical Earth displaced earlier beliefs in a flat Earth: In early Mesopotamian mythology, the world was portrayed as a flat disk floating in the ocean with a hemispherical sky-dome above, and this forms the premise for early world maps like those of Anaximander and Hecataeus of Miletus. Other speculations on the shape of Earth include a seven-layered ziggurat or cosmic mountain, alluded to in the Avesta and ancient Persian writings.
  The realization that the figure of the Earth is more accurately described as an ellipsoid dates to the 17th century, as described by Isaac Newton in Principia.
context_section_description: A meridian of longitude is a line where local solar noon occurs at the same time each day. These lines define "north" and "south". These are perpendicular to lines of latitude that define "east" and "west", where the Sun is at the same angle at local noon on the same day. If the Sun were travelling from east to west over a flat Earth, meridian lines would always be the same distance apart - they would form a square grid when combined with lines of latitude. In reality, meridian lines get farther apart as one travels toward the equator, which is only possible on a round Earth. In places where land is plotted on a grid system, this causes discontinuities in the grid. For example, in areas of the Midwestern United States that use the Public Land Survey System, the northernmost and westernmost sections of a township deviate from what would otherwise be an exact square mile. The resulting discontinuities are sometimes reflected directly in local roads, which have kinks where the grid cannot follow completely straight lines.
  Mercator projection has notable examples of size distortions.
caption: Diagram showing how the interior angles of triangles add up to about 180° when plotted on a small, nearly flat area of the Earth, but add up to more than 180° (in this case 230°) when plotted on a large area with significant curvature
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